X-Ray Micro-Beam Production and High Brilliance X-Ray Production

ABSTRACT

An x-ray micro-beam radiation production system is provided having: a source of accelerated electrons, an electron focusing component configured to focus the electrons provided by the source, and a target which produces x-rays when electrons impinge thereon from the source. The electron focusing component is configured to focus the electrons provided by the source such that they impinge at a focal spot having a width δ formed on a surface of the target. The focusing component is configured to move the electron beam relative to the target such that the focal spot moves across the target surface in the width direction, and/or the target is movable relative to the focusing component such that the focal spot moves across the target surface in the width direction, the surface velocity of the focal spot across the target surface in the width direction being greater than vt where:formula (I), k, ρ and c denoting respectively the heat conductivity, the density and the heat capacity of the target material, and d denoting the electron penetration depth in the target material.vt=π⁢k4⁢ρ⁢c·δd2,

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. application Ser. No.16/308,780, filed Dec. 10, 2018, which is a U.S. national stage entry ofInternational Application No. PCT/GB2017/051733, filed Jun. 14, 2017,which claims the benefit of GB 1617330.4, filed Oct. 12, 2016 and GB1610646.0, filed Jun. 17, 2016, the disclosures of each of which areincorporated herein by reference.

FIELD OF THE INVENTION

The present invention relates to the production of x-ray micro-beamradiation and to the production of high brilliance x-rays.

BACKGROUND

X-ray micro-beam radiation, i.e. x-ray radiation with a beam width inthe order of microns, has been found to have a very limited effect onhealthy living tissue at doses that, were they supplied by normal (i.e.macro-beam) radiation, would result in substantial tissue damage. Normaltissue can tolerate an x-ray micro-beam radiation dose in the order ofthousands or even ten thousands of Grays. In contrast, cancerous tissueis more susceptible to x-ray micro-beam radiation. Accordingly, adistinct advantage of a treatment with x-ray micro-beam radiation isthat healthy tissue surrounding the dosage site easily tolerates theradiation, and any collateral damage is rapidly repaired. Therefore,x-ray micro-beam radiation can be used as an effective form ofradiotherapy to treat cancerous tissue.

In order to preserve the micro-beam structure in the tissue, shortexposure times and parallel beams are required. Conventionally, in orderto generate x-ray micro-beams with a sufficiently high dose rate,synchrotron radiation has been used. For example, facilities such as theEuropean Synchrotron Radiation Facility (ESRF) in Grenoble, France,provide parallel x-ray beams with a dose rate of around 15,000 Gy/s andaverage photon energy of around 100 keV. However, such facilities arestatic complexes measuring many hundreds of meters in diameter, andtherefore are clearly impractical for a widespread clinical applicationof micro-beam radiation therapy.

It would thus be desirable to be able to provide a system for generatingx-ray micro-beams, which is significantly smaller, cheaper and lesscomplex than a synchrotron.

Soft tissue contrast in conventional medical x-ray imaging based on tinychanges in the absorption coefficient is usually poor, phase contrastimaging, measuring the much larger relative differences in therefractive index, can provide significantly better contrast (Pfeiffer F,Weitkamp T, Bunk O, David C. Phase retrieval and differentialphase-contrast imaging with low-brilliance X-ray sources. Naturephysics. 2006; 2(4):258-61). Various methods have been used for phasecontrast imaging (Momose A. Phase-sensitive imaging and phase tomographyusing X-ray interferometers. Optics Express. 2003; 11(19):2303-14), butall are based on the interferometric measurement of phase shifts inducedby refractive index variations in the imaged object. The prerequisite toobserve interference is the coherence of the radiation source. Whereastemporal coherence can be obtained with the aid of crystalmonochromators, spatial coherence is much more delicate as path lengthdifferences between photons emitted from different parts of the x-raysource have to be much smaller than the wavelength λ measuring in theorder of only 10⁻¹¹ m for hard x-rays. In order to achieve spatialcoherence in conventional x-ray tubes, gratings have been proposed andused (Pfeiffer et al., ibid.) that absorb a substantial part of theinitial x-ray beam intensity.

The beam quality of an x-ray source is usually characterised by itsbrilliance B, a quantity that measures the number of photons N emittedper time dt, area dA, emission angle interval dΩ and frequency intervaldv,

$B = {\frac{dN}{{{dt} \cdot d}\;{\Omega \cdot {dA} \cdot d}\;\nu}.}$

Due to beam divergence, broad photon energy spectra, large focal spotwidths and a low electron to photon conversion efficiency, the radiationconventionally generated by x-ray tubes has only a low brilliance and istherefore unsuitable for applications such as phase contrast imaging, orother high resolution x-ray imaging.

X-ray radiation of high brilliance can be generated with synchrotrons.However, as discussed above, suitable synchrotrons are large, expensivefacilities and are impractical for many applications especially in themedical field.

It would thus also be desirable to be able to provide a system forgenerating high brilliance x-rays, which is significantly smaller,cheaper and less complex than a synchrotron.

SUMMARY

In general terms, the present invention provides an x-ray radiationproduction system having:

-   -   a source of accelerated electrons;    -   an electron focusing component configured to focus the electrons        provided by the source; and    -   a target which produces x-rays when electrons impinge thereon        from the source;    -   wherein the electron focusing component is configured to focus        the electrons provided by the source such that they impinge at a        focal spot formed on a surface of the target.

In a first aspect the invention provides an x-ray micro-beam radiationproduction system having:

-   -   a source of accelerated electrons;    -   an electron focusing component configured to focus the electrons        provided by the source;    -   a target which produces x-rays when electrons impinge thereon        from the source; and    -   a collimator having one or more micro-beam forming apertures        which collimate the produced x-rays into one or more respective        micro-beams, the, or each, micro-beam forming aperture having a        given shape on a cross-section therethrough perpendicular to the        formed micro-beam;    -   wherein the electron focusing component is configured to focus        the electrons provided by the source such that they impinge at a        focal spot formed on a surface of the target, the focal spot        having substantially the same shape as a projection of the        cross-sectional shape of the aperture(s) onto the target surface        at the focal spot.

By focusing the electrons such that the focal spot has substantially thesame shape as the projection of the cross-sectional shape of the, oreach, micro-beam forming aperture, partial shadowing of the source alongthe micro-beam path behind the collimator can be avoided and the doserate considerably increased. Moreover, in contrast to a micro-focusx-ray tube, the heat load can be spread over a larger area of thetarget, and the power of the source can hence be increased.

In a second aspect, the invention provides a method of operating thesystem of the first aspect having the steps of:

-   -   providing electrons from the electron source;    -   focusing the electrons using the electron focusing component        such that they impinge at the focal spot formed on the surface        of the target, thereby producing x-rays; and    -   collimating the resulting x-rays using the collimator thereby        producing x-ray micro-beam radiation.

In general, the term micro-beam may be understood to mean a narrow beamof radiation with micrometre or sub-millimetre dimensions. Moreover,when there is more than one micro-beam, any two adjacent micro-beams maybe substantially parallel.

Optional features of the invention, and particularly of the first andsecond aspects of the invention, will now be set out. These areapplicable singly or in any combination with any suitable aspect of theinvention.

The source may include an accelerator to accelerate the electrons. Inthis case, the target may be electrically neutral. However,alternatively or additionally, the target may be an anode to (further)accelerate the electrons.

The electron focusing component may be configured to focus the electronsprovided by the source such that substantially all the focused electronsimpinge on the focal spot of the target surface.

The target may be moveable relative to the focusing component such thatthe focal spot moves across the target surface. Additionally oralternatively, the focussing component may be configured to move theelectron beam relative to the target such that the focal spot movesacross the target surface. Either of these features may aidheat-dissipation through the target and may stop over-heating of thetarget at any particular point.

The target may be cylindrical, and the target may rotate around its axisto move the target relative to the focusing component. The target mayrotate to provide a speed of movement of the focal spot over the targetsurface of at least 50 m/s, and preferably at least 100 or 150 m/s.

The electron source, the focusing component, and the target may betranslated with a reciprocating motion (e.g. along the cylinder axis ofa cylindrical target), and the focusing component may be configured toapply an equal but opposite reciprocating motion of the impingementposition of the electrons on the target.

The, or each, aperture in the collimator may be a slit, and the focalspot may be correspondingly elongate in shape. In this case, the lengthdirection of the slit(s) and the length direction of the focal spot canbe parallel. This enables an even greater proportion of the x-rayradiation produced by the electrons impinging on the focal spot to bedirected through the slit(s). More particularly, the slits may berectangular in cross-section. When the target is cylindrical, the lengthdirection of the focal spot can be parallel to the cylinder axis. Theshortest dimension (the width) of the focal spot may be less than 1 mm,and preferably is less than 100 μm or less than 50 μm. The cross-sectionof the, or each, slit may have a width of at least 20 μm, and preferablythe width is around 50 μm. The cross-section of the, or each, slit mayhave a width of at most 500 μm, and preferably at most 100 μm.

There may be plural apertures, and the centre-to-centre (ctc) distancebetween adjacent apertures may be at least 100 μm, and preferably atleast 200 μm. The ctc distance may be at most 4000 μm, and preferably atmost 800 μm.

The electrons may impinge on the target surface at a target angle, andthe target angle may be controlled by the focusing component to be nomore than 20° from the normal to the target surface at the focal spot.Preferably, the target angle may be no more than 10°.

The electrons may be accelerated with an acceleration voltage of atleast 100 kV, preferably at least 400 kV, and most preferably at least500 kV. The potential is typically limited by a high voltage supply andachievable electron currents.

The micro-beam radiation produced by the collimator may have a beamwidth of at least 20 μm, and preferably at least 50 μm. The beam widthmay be no more than 500 μm, and preferably no more than 100 μm.

The collimator may be spaced by a distance of at least 10 cm and/or atmost 1 m from the focal spot.

The target may be made of tungsten or tungsten alloy. In some examples,the outer surface of the target may be formed of tungsten or a tungstenalloy and the core of the target is formed of copper. This can reduceweight and increase heat conduction. The outer surface of the target mayhave of a thickness of at least 5 mm and/or at most 10 mm.

The collimator may be at an angle to the normal to the target surface atthe focal spot of at least 40° and/or at most 80°, e.g. an angle ofaround 60° may be suitable.

At a distance of 500 mm from the target, the micro-beam(s) formed by thecollimator may deliver a radiation dose rate of at least 1 Gy/s. At adistance of 500 mm from the target, the micro-beam(s) formed by thecollimator may deliver a radiation dose rate of no more than 1200 Gy/s.Herein, references to “dose” and “dose rate” refer to an entrance doseto water in 5 mm depth.

The x-rays collimated by the collimator may have a mean energy of atleast 60 keV and/or at most 300 keV. The system may further have afilter (e.g. an aluminium or copper filter) between the target and thecollimator. This can help to filter out low energy photons produced atthe target by the impinging electrons.

In a third aspect, the present invention provides an x-ray radiationproduction system having:

-   -   a source of accelerated electrons;    -   an electron focusing component configured to focus the electrons        provided by the source; and    -   a target which produces x-rays when electrons impinge thereon        from the source;    -   wherein the electron focusing component is configured to focus        the electrons provided by the source such that they impinge at a        focal spot having a width δ formed on a surface of the target;        and    -   wherein the focusing component is configured to move the        electron beam relative to the target such that the focal spot        moves across the target surface in the width direction, and/or        the target is movable relative to the focusing component such        that the focal spot moves across the target surface in the width        direction, the surface velocity of the focal spot across the        target surface in the width direction being greater than v_(t)        where:

${v_{t} = {\frac{\pi k}{4\rho c} \cdot \frac{\delta}{d^{2}}}},$

k, ρ and c denoting respectively the heat conductivity, the density andthe heat capacity of the target material, and d denoting the electronpenetration depth in the target material.

In particular, for a given target and electron beam energy, by adoptinga suitably small focal spot width δ and/or a suitably high surfacevelocity of the focal spot across the target surface v_(t), a change inthe physics of the target heating can be induced. This change enableshigher electron beam intensities at the focal spot. The system can thusserve as a suitable and powerful compact x-ray source in phase contrastimaging and microbeam radiation therapy. The electron penetration depthd may be defined as

$E_{el}/\left( {{\left( {\frac{\delta E_{ei}}{\delta z}(z)} \right)\max},} \right.$

where E_(el) is the average kinetic energy absorption of an electron,dE_(el)/dz(z) is the kinetic energy absorption per depth interval, and zis distance into the target from the surface.

In a fourth aspect, the invention provides a method of operating thesystem of the third aspect having the steps of:

-   -   providing electrons from the electron source;    -   focusing the electrons using the electron focusing component        such that they impinge at a focal spot having a width δ formed        on the surface of the target, thereby producing x-rays; and    -   moving the electron beam relative to the target such that the        focal spot moves across the target surface in the width        direction, and/or moving the target relative to the focusing        component such that the focal spot moves across the target        surface in the width direction, the surface velocity of the        focal spot across the target surface in the width direction        being greater than v_(t) where:

${\nu_{t} = {\frac{\pi k}{4\rho c} \cdot \frac{\delta}{d^{2}}}},$

k, ρ and c denoting respectively the heat conductivity, the density andthe heat capacity of the target material, and d denoting the electronpenetration depth in the target material.

The system of the third aspect may be used to perform imaging, such ashigh resolution or phase contrast imaging. For example, a method ofphase contrast imaging has the steps of: performing the method of thefourth aspect; and performing imaging using the produced x-rays as asource of illumination.

Optional features of the invention, and particularly of the third andfourth aspects of the invention, will now be set out. These areapplicable singly or in any combination with any suitable aspect of theinvention.

The source may include an accelerator to accelerate the electrons. Inthis case, the target may be electrically neutral. However,alternatively or additionally, the target may be an anode to (further)accelerate the electrons.

The electron focusing component may be configured to focus the electronsprovided by the source such that substantially all the focused electronsimpinge on the focal spot of the target surface.

The surface velocity of the focal spot across the target surface in thewidth direction may be at least two times greater than v_(t).

The width δ of the focal spot may be less than 100 μm, and preferably isless than 10 μm or less than 1 μm.

The target may be cylindrical, and the target may rotate around its axisto move the target relative to the focusing component. The target mayrotate to provide a surface velocity of at least 100 m/s, and preferablyat least 200 or 500 m/s.

The electrons may impinge on the target surface at a target angle, andthe target angle may be controlled by the focusing component to be nomore than 20° from the normal to the target surface at the focal spot.Preferably, the target angle may be no more than 10°.

The electrons may be accelerated with an acceleration voltage of atleast 40 kV.

Target materials may have spectral lines that enhance the beambrilliance at certain energies such as the Kα1 line of tungsten at59.318 keV. Characteristic x-rays of a spectral line of the targetmaterial at around 60 keV may have a spatial coherence length of atleast 5 μm at 1 m distance from the target, and preferably of at least10 μm.

The produced characteristic x-rays of a spectral line of the targetmaterial at around 60 keV may have a photon flux of at least 1·10⁶ mm⁻²s⁻¹ at 1 m distance from the target, and preferably of at least 1·10⁷mm⁻² s⁻¹ or at least 1·10⁸ mm⁻² s⁻¹.

The target may be made of tungsten or tungsten alloy. In some examples,the outer surface of the target may be formed of tungsten or a tungstenalloy and the core of the target is formed of copper. This can reduceweight and increase heat conduction. The outer surface of the target mayhave a thickness of at least 5 mm and/or at most 10 mm.

The system may further have either:

-   -   (A) a collimator having one or more micro-beam forming apertures        which collimate the produced x-rays into one or more respective        micro-beams, the, or each, micro-beam forming aperture having a        given shape on a cross-section therethrough perpendicular to the        formed micro-beam, wherein the focal spot has substantially the        same shape as a projection of the cross-sectional shape of the        aperture(s) onto the target surface at the focal spot; or    -   (B) no collimator to collimate the produced x-rays, or a        collimator other than collimator (A).

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described by way of examplewith reference to the accompanying drawings in which:

FIGS. 1A and 1B (from Zeman et al. Radiation Res. 15 (1961), 496) show,respectively, the effects of ionising radiation on biological tissue.

FIG. 2A is a front-on schematic view of an x-ray micro-beam radiationproduction system and FIG. 2B is a side-on schematic view.

FIG. 3 is a schematic view of a collimator of the system and part of atarget of the system.

FIG. 4 is a schematic plan view of the collimator.

FIG. 5 is a partial cross-section of the collimator.

FIG. 6 is a schematic view of the surface of the target.

FIG. 7 is a plot of photon yield as a function of electron incidenceangle and photon emission angle.

FIG. 8 compares the photon count spectrum of a 600 kV x-ray tube and thesynchrotron beam of ID17 at the European Synchrotron.

FIG. 9 shows profiles of photon fluence perpendicular to a micro-beamaxis for various patient treatment depths at a focal spot to collimatordistance of 500 mm.

FIG. 10 shows profiles of photon fluence along the micro-beam length forvarious patient treatment depths at a focal spot to collimator distanceof 500 mm.

FIG. 11 is a plot of radiation dose against depth for a number ofradiation sources.

FIG. 12 shows the depth dependent energy deposition of a 600 keVelectron beam in tungsten.

FIG. 13 is a log-log plot of rotational speed against power of theelectron beam.

FIG. 14 shows plots of average and peak surface temperatures againsttime for a 500 kW x-ray tube, various target radii at 178 m/s surfacevelocity of the rotating target, a focal spot length of 2 cm and noreciprocating motion of the target.

FIG. 15 shows plots of average and peak surface temperatures againsttime for a 712 kW x-ray tube, various target radii at 178 m/s surfacevelocity of the rotating target, a focal spot length of 2 cm and noreciprocating motion of the target.

FIG. 16 shows profiles of photon fluence rate perpendicular to amicro-beam axis for various patient treatment depths at a focal spot tocollimator distance of 500 mm, and a larger focal spot size than that ofFIG. 9.

FIG. 17 shows x-ray tube performance at different focal spot widths andacceleration voltages: The maximum possible electron beam power of thex-ray tube is shown in a colour scale at a surface velocity of 200 m/sand a maximum temperature increase of 2500 K in the focal spot. Thedashed line is the width-voltage contour for the transition from heatconduction limit to heat capacity limit at a surface velocity of 200m/s, and the solid contour lines show the corresponding transitions fromheat conduction limit to heat capacity limit at selected other surfacevelocities.

FIG. 18 shows a performance comparison of various x-ray sources: A linefocus tube (LFT) according to the present invention is compared to 3rdgeneration synchrotrons, Inverse Compton Scattering Sources and varioustypes of x-ray tubes at a photon energy of 60 keV. Sources shown indashed regions usually do not reach 60 keV.

FIG. 19A shows the geometry at the anode surface for electron beamenergy absorption in the target material. A thin electron beam thatmoves along the x-axis hits the target material and causes a powerdistribution in the target material. FIG. 19B depicts the energyabsorption per depth interval for a 500 keV electron beam in tungsten.The maximum of the energy absorption at around 10 μm depth can be usedto calculate the electron penetration depth d.

FIG. 20A shows the geometry used for a Monte Carlo study of the focalspot size in a simulation of the electron scattering limit of the focalspot width. An electron beam hits the surface of the tungsten target. Atan observer position the trajectories of created photons are recordedand their origin in the x′-y′ plane calculated. FIG. 20B presents aprofile of the photon origin along the x′ axis.

FIG. 21 shows efficiency of electron to photon conversion in a tungstentarget. The conversion efficiency is defined as the number of photons atthe tungsten Kα1 fluorescence line emitted per electron. It is zerobelow and strongly increasing with electron energy above 59.3 keV.

DETAILED DESCRIPTION AND FURTHER OPTIONAL FEATURES

We describe below in a first subsection the production of x-raymicro-beam radiation and then in a second subsection the production ofhigh brilliance x-rays.

Production of X-Ray Micro-Beam Radiation.

With reference to FIGS. 1A and 1B, there are shown two biologicalsamples (from Zeman et al. Radiation Res. 15 (1961), 496) which havebeen exposed to ionising radiation. The sample tissue 101 in FIG. 1A hasbeen exposed to radiation with a dose of 140 Gy, with a beam width of 1mm. As can be seen, a region 102 of the tissue has been destroyed and a1 mm wide void is left within the tissue. However a substantial amountof surrounding tissue 103 has also been injured, which was not withinthe area directly exposed to ionising radiation. In contrast, abiological sample 104 as shown in FIG. 1B was exposed to ionisingradiation with a dose of 4000 Gy but with a beam width of 25 μm. Thebiological material within area 105, shows a reduction of cell nuclei.However the tissue structure stays intact. This demonstrates thatradiation of a small beam width (e.g. less than 1000 μm) results in asubstantial reduction in collateral damage to surrounding tissue.Further, a much higher radiation dose, 4000 Gy as compared with 140 Gy,is required to destroy the targeted tissue. This is known as the dosevolume effect i.e. as the volume of irradiated tissue decreases theradiation dose required to cause damage to that tissue increases.

Moving to FIGS. 2A and 2B, a system 200 for producing x-ray micro-beamradiation is shown. More particularly, FIG. 2A shows a front-on view ofparts of the system in which the micro-beam radiation is emitted in aplane coming out of the page at an angle β, and FIG. 2B shows a side-onview of the system.

Considering first FIG. 2A, an electron source 201, which might forexample be a thermionic electron gun, provides a beam of acceleratedelectrons 202 which enter an electron focusing component 203. Theelectron focusing component could, in some examples, be a set of magnetssuitable for bending and shaping the beam of electrons throughapplication of a magnetic force. The result of the focusing is a focusedelectron beam 204, which impinges at a focal spot 206 on a surface of acylindrical target 205. The target can be, for example, a cylinder witha tungsten or tungsten alloy outer layer and a copper core. The copperpromotes heat transfer from the target surface, which is heated by theimpinging electrons. There is a distance 207 between the target and thesource of electrons, which in this example, is about 500 mm. The focalspot can be generally rectangular with its long axis parallel to theaxis of the cylindrical target, and may move along a direction 208parallel to the cylindrical axis. As the focused electron beam impingeson the target, it causes x-rays to be emitted therefrom in a manner wellunderstood for x-ray tube devices. The electrons may be accelerated byan accelerator, e.g. contained in the electron source, so as to increasethe energy of the electrons as they impinge on the target. Theaccelerator may use a voltage of around 600 kV to accelerate theelectrons. Additionally or alternatively, the target may be an anodetarget to (further) accelerate the electrons.

Turning then to FIG. 2B, as indicated by the arrow, the target canrotate around its cylindrical axis. Also shown in FIG. 2B are: a vacuumhousing 213 for the source 201, electron focusing component 203 andtarget 205; an exit window 214 from the housing; and a multi-slitcollimator 212, which forms micro-beams by collimating an angular sector210 of the x-rays emitted from the target and passing through the exitwindow. In this example the collimator is around 500 mm from the surfaceof the target, although this can be adjusted. The x-rays emitted fromthe target have generally diverging beam paths, although increasing thedistance of the collimator from the focal spot reduces the divergence inthe formed micro-beams. An angle β exists between a normal to the targetsurface at the focal spot of the impinging electrons and the collimatedpart of the emitted x-rays. Similarly, an angle α exists between theincident focused electrons 204 and a normal to the target surface at thefocal spot. α can have a value of around 10° and β can have a value ofaround 60°.

Rotating the cylindrical target 205 moves the focal spot 206 over thesurface of the target, and thus helps to prevent the target locallymelting at the focal spot. Similarly, moving the focal spot along thedirection 208 parallel to the cylindrical axis of the target helps tospread the heat load over a larger area and prevent target melting. Ingeneral it is beneficial to adopt both types of movement. The axialmovement can, for example, conveniently be achieved by magnetic electronbeam deflection in component 203 producing a reciprocating motion of thefocal spot over the target cylinder surface. Then, in order to keep theemitted x-rays fixed in space, the whole system, except for thecollimator 212, is translated synchronously with an equal and oppositereciprocating motion such that the focal spot 206 remains stationary. Analternative of reciprocating just the target would be possible, butproducing a superposition of target rotation and translation within thevacuum of the housing might actually be more challenging thantranslating the whole housing.

When the electron source 201 is based on thermionic emission, its outputcan be described by the Richardson Equation:

$j = {A_{0}T^{2}e^{- \frac{W}{kT}}}$

Where A₀ is a constant with value 60 Acm⁻² K⁻²; W is the work functionof the metal used in the electron gun (in this case 4.5 eV), k is theBoltzmann constant, and T is the temperature of the metal. For T=2700 K,j=1.75 A/cm² and for T=3000 K (the likely limit of a cathode), j=14.9A/cm².

It should be noted that Schottky emission is not taken into account inthe above. Therefore j may have a slightly higher value in actualitythan discussed above. Also, space charge will not be an importantconsideration. As the electrons may be accelerated across a voltage of600 kV, the system is being operated in its saturation region (i.e.where an increase in acceleration voltage does not result in anysubstantial increase in electron current, see the space charge law).Hence a 1.0 cm² filament surface would be sufficient to produce anelectron beam of more than 1 A at a surface temperature of 2700 K.

The electron beam 202 will have an intensity Φ, where

$\Phi = {\frac{I}{8\pi^{2}\epsilon_{x}\epsilon_{y}}.}$

When the electron source 201 is a thermionic electron gun, thenormalised emittance of the electron beam 202 at 3000K can be describedas follows:

$\epsilon_{N} = {{\sigma_{x}\sqrt{\left( \frac{k_{b}T}{m_{e}c^{2}} \right)}} = {{7.11 \cdot 10^{- 4}}\sigma_{x}}}$

Where m_(e) is the mass of an electron (9.11×10⁻³¹ kg), c is the speedof light in vacuum, and σ_(x) is the root-mean-square beam size.

Therefore, in the case of a 20 mm diameter source, the emittance can becalculated as ϵ_(N)≈7.1 mm·mrad. This value is quite conservative, andit is likely that the emittance can be decreased.

It is also helpful to consider the minimum spot size that the beam canbe focused onto. The geometric emittance ϵ can be calculated as follows:

${{\epsilon = \frac{\epsilon_{N}}{\gamma\beta}};{{\gamma\beta} \approx {{1.1}33}};}\therefore{\epsilon \approx {6.27{{mm} \cdot m}{rad}}}$

For a 100 μm width focal spot, the divergence in this example would be0.0627 rad=3.59° at the focal spot. Therefore the beam may have to hitthe target surface such that the long axis of the rectangular focal spotis perpendicular to the incoming electron beam.

Moving now to the collimator 212, this is shown in more detail in FIG.3, along with an extract of the target 205 surface. The collimatorcomprises a number of slits 301 and blanks 302. The slits are generallyrectangular in cross-section to have substantially the same shape as therectangular focal spot 206 when they are projected onto the targetsurface. The slits may thus have a cross-sectional width of 50 μm inthis example to produce a projected width of about 100 μm, i.e. the samewidth as the focal spot. Shaping the collimator openings such that theirprojections are congruent with the focal spot helps to avoid partialshadowing of the source along the micro-beams downstream of thecollimator. The photon fluence in the micro-beams can hence be equal toan open field geometry.

Further details of the collimator are shown in FIGS. 4 and 5. Generallythe collimator 212 is formed from a large plate of a suitable materialto absorb incident x-rays e.g. lead. As shown in the plan view of FIG.4, an array of slits 301 is provided in the plate. The collimator istypically configured for a given focal spot to collimator distance,which in this example is 7 cm. The array is around 20×20 mm², andcomprises forty-nine 50 μm wide and 20 mm long slits. A schematicpartial cross-section of the collimator plate is shown in FIG. 5.Especially for short focal spot to collimator distances and for thickcollimators the slits can have an inclination towards the perpendicularof the collimator surface in order to account for the divergence of theradiation field. Wire cutting can be used to form the collimator slits.In particular, small holes can be drilled at opposing ends of the array,and the cutting wires inserted therethrough.

As was shown in FIG. 2B, and is further illustrated in FIG. 6, an angleα exists between a normal to the target 205 surface at the focal spotand the incident electron beam e⁻. This angle α is referred to as theincident angle. Similarly, there is an angle β between the normal to thetarget at the focal spot and an emitted x-ray beam γ. This angle β isreferred to as the emission angle. FIG. 7 shows a plot of photon yield(in parts per million) as a function of both incidence and emissionangles. The region 701 shows the largest photon yield of around 700-800ppm, and region 702 shows the smallest yield of between 50-200 ppm. Thisplot demonstrates that for an incidence angle of 10° or less a goodphoton yield can be achieved across a relatively broad range of emissionangles (e.g. −60° to +60°). Generally it can be stated that the plotshows that photon intensity is high for small incidence angles and thatperpendicular to the plane shown in FIG. 6 the intensity followsLamberts law:

I(θ)=I ₀ cos(θ)

Where θ is the angle relative to the plane in FIG. 6 and I₀ is theintensity for θ=0.

FIG. 8 compares the photon count spectrum of a 600 kV x-ray tube(tungsten target, 1 mm Al filtering) and the synchrotron beam of ID17 atthe European Synchrotron presently used for most preclinical micro-beamirradiations. Line 1001 is the synchrotron spectrum (see e.g. Crosbie etal., J. Synchrotron Rad. 22, 1035-1041 (2015)). The beam is peaked ataround 80 keV and has a mean energy of 110 keV. There is no significantcontribution of photons with energy below 40 and above 300 keV. Whereas,line 1002 shows the spectrum of a 600 kV x-ray tube of a type which maybe used in the present invention. The spectrum is significantly widerthan the synchrotron spectrum and a significant photon contribution isexpected between 25 and 500 keV. The mean energy is around 149.2 keV,18.3% of the primary beam being absorbed by the Al filtering.

Table 1 below shows in column 2 the measured dosage rate of aconventional 160 kV x-ray tube with a power of 1.8 kW, a tungsten targetand a 1 mm thick Al filter for distances of between 100 and 500 mm. Asshown in column 3, a dosage rate per kW can thus be estimated for theconventional tube. From these measurements the expected dose rate per kWfor the micro-beam radiation production system described above can becalculated by Monte Carlo simulations. Due to an increased efficiency inthe electron-photon conversion in the target and higher photon energiesthe dose rate is expected to be 16.2 times higher. The expected doserates per kW for the system can be found in column 4. As discussedlater, the maximum power of the system is limited by the surfacevelocity of the rotating anode. Assuming a surface velocity equivalentto that of a standard spinning disk x-ray tube anode of 178 m/s thepower limit would be 712 kW. This leads to maximum expected dose ratesof between 3660 Gy/s and 147 Gy/s at distances between 100 and 500 mmfrom the focal spot, as indicated in column 5.

TABLE 1 Distance Dosage rate at 160 Dosage rate at 160 kV Dosage rate at600 Dosage rate at 600 kV [mm] kV and 1.8 kW [Gy/s] and 1 kW [Gy/s] kVand 1 kW [Gy/s] and 712 kW [Gy/s] 100 0.5715 0.3175 5.14 3660 200 0.14290.0794 1.29 919 300 0.0635 0.0353 0.572 407 400 0.0357 0.0198 0.321 229500 0.0229 0.0127 0.206 147

Moving to FIG. 9, this shows absorber free photon fluence cross-sectionsperpendicular to a single beam of micro-beam radiation as produced bythe system discussed above for a focal spot to collimator distance of500 mm at different patient treatment depths. The photon fluence isrelative to the open field, i.e. it has been normalised relative tonon-collimated radiation. As compared to parallel synchrotron radiation,the x-ray source of the system will cause beam penumbras with distancefrom the collimator. The six lines in the plot, show the effect on thephoton fluence profile for a number of depths (distances betweencollimator and measurement point) relevant in patient treatment. As iscommon to all of the lines, the relative fluence in the beam is 1,meaning the absence of any partial source shadowing. This shows that themicro-beam radiation produced by the system can provide dose profileswith sufficiently sharp beam penumbras. Even at 30 cm depth the width ofthe penumbra is just 30 μm and hence much smaller than peak-to-peakdistance of around 400 μm.

FIG. 10 shows absorber fluence profiles along the length of themicro-beam. As with FIG. 9, six lines are shown, each corresponding to adifferent patient treatment depth. The beam divergence also affects thelength of the micro-beams. For example, the narrowest radiation doseprofile (corresponding to 5 cm treatment depth) has a total dose profilewidth of around 26 mm.

Table 2 below shows the change in centre-to-centre distance, beam width,and beam penumbra with varying focal spot to collimator distance:

TABLE 2 Distance Centre- Beam [mm] to-centre [μm] Beam width [μm]penumbra [μm] 0 400 50 0 50 440 55 5 100 480 60 10 150 520 65 15 200 56070 20 250 600 75 25 300 640 80 30 350 680 85 35

It should be noted that FIGS. 9 and 10 only take into account primaryphoton fluence (photon rate per surface unit area) and assume a perfectabsorber (i.e. 100% absorption in the collimator material). Scatteringwas not taken into account.

FIG. 11 is a plot of dose as a function of depth into a specimen forthree different radiation sources. In all cases, the specimen was water.The depth dose curve for radiation produced at the European SynchrotronRadiation Facility (ESRF) is denoted by line 1401. The line 1402 shows adepth dose curve for radiation produced with parallel beams and with anx-ray tube spectrum. As can be seen, this source provides a greater doserelative to the ESRF source as a function of depth. However trulyparallel beams, such as might be provided by a synchrotron radiationsource, cannot be produced by an x-ray tube. Line 1403 indicates a depthdose curve for an x-ray tube with diverging beams, starting at adistance of 50 cm from the target surface. All of the dose curves havebeen normalised relative to their respective maximum values. As is shownby the plots in FIGS. 9, 10, and 11 the beam shapes and depth dosecurves are very similar to those produced at the ESRF. The x-ray tubebeam penumbras remain acceptably small, although they are slightly widerthan those seen at the ESRF.

It is useful at this stage to discuss the concept of the efficiency ofan x-ray tube. Generally, this can be defined as η, where η=EnergyUsed/Grays Produced. From Table 1, for a 600 kV x-ray tube at a distanceof 500 mm, η can be calculated as η=4.85 kJ/Gy. From this value for η,it can be seen that to produce a 500 Gy peak entrance dose at 500 mm,which would approximately be required for a micro-beam treatment, 2.425MJ are required. Most of this energy will be deposited as heat into thetarget. This is sufficient energy to heat 6.5 kg tungsten up to itsmelting point. This energy needs to be efficiently dissipated whenworking at high dose rates.

To investigate the temperature rise of the focal spot on a rotatingtarget, the Oosterkamp (1948) equation can be used,

${{\Delta T} = {\frac{2P}{A}\sqrt{\frac{\Delta t}{\pi k\rho c}}}},$

where ΔT is the change in temperature, P is the power of the electronbeam, A is the area of the focal spot, and Δt is the dwell time. Fortungsten the specific heat capacity c=138 J/(kg·K); thermal conductivityk=170 W/(m·K); and density ρ=19.3 g/cm⁻³. For a target which isrotating,

${{\Delta t} = \frac{2\delta}{v}},$

where v is the surface velocity of the target and δ is the focal spotwidth.

Therefore, rearranging the Osterkamp equation, for a maximum ΔT at thesurface velocity of the target, v is given by v=αP² where α is aconstant. Assuming a tungsten target with a 100 μm wide and 20 mm longfocal spot (and a 60° emission angle and therefore a 50 μm slit width)

$\alpha = {0.0225 \cdot {\frac{m/s}{{kW}^{2}}.}}$

The Osterkamp equation can be derived by solving the heat equationassuming that the heat is supplied at the target surface only (Neumannboundary condition). This assumption is valid as long as the heatdiffusion range, while a certain point on the surface is hit by theelectron beam, is much larger than the electron penetration depth intothe target material.

If this assumption cannot be made, i.e. at very high surface velocities,the electron absorption volume acts as a source within the targetmaterial. The heating is then much faster than the heat conduction, andtherefore the relation Pδt=ρcVΔT can be used, where V is the electronabsorption volume. FIG. 12 shows a depth dose curve of 600 keV electronsimpinging on the target. From this a maximum penetration depth of 30 μmis a reasonable and conservative assumption. Using otherwise the samedimensions above:

V≈20 mm×100 μm×30 μm

$v = {{\frac{2\delta}{\rho Vc\Delta T}P} = {0.25 \cdot \frac{\frac{m}{s}}{kW} \cdot P}}$

From this consideration it follows that the target heating will alwaysbe limited by the most rapid of the two above processes.

This can be seen in FIG. 13, which is a log-log graph of the rotationalspeed required for the target to stay below 2500 K as a function of thepower of the electron beam. Line 1501 presents the Oosterkamp curve,where target heating is limited by heat conduction, while line 1502corresponds to the high velocity domain, where target heating is limitedby the heat capacity of the target material. Line 1501 is proportionalto P² and therefore steeper than line 1501, which is just proportionalto P. Line 1503 shows the actually required surface speed depending onthe power of the electron beam. A more detailed discussion of theproduction of high brilliance x-rays using target heating limited by theheat capacity is provided in the next subsection.

Conventionally, x-ray tubes using a spinning disk target can spin atrates of up to 17,000 rpm. Assuming a 100 mm radius disc, this wouldresult in a surface velocity of the target of around 178 m/s which wouldresult in a power limit of the x-ray tube of around 712 kW. This isclearly in the linear part of the required surface-speed to powerrelation. To operate at this power level in a 600 kV x-ray tube wouldrequire an electron current of around 1.19 Amps. It may be possible torotate the target such that it has a much higher surface velocity of 800m/s, at such speeds it would be possible to have a 3 MW output. In thefollowing, a conservative maximum power of 712 kW for the system will beassumed.

It is also important to take into account the cooling of the targetwhilst it is not being exposed to the electron beam. After one rotation,the surface of the target will have cooled down to approximately:

${T = {{0.5T_{R}\sqrt{\frac{\delta}{\pi R}}} = {15.77K}}};$

where T_(R) is the initial temperature (i.e. 2,500K), δ is assumed to be50 μm, and the radius of the target R is assumed to be 0.1 m. After eachrevolution of the target, the surface temperature will increase.

For longer time periods the heat equation needs to be solved. Results ofsolving the heat equation for this situation are shown in FIGS. 14 and15 for a 500 kW and 712 kW x-ray tube respectively. In these plots thedotted lines indicate the temperature of the surface of the target justafter it was hit by the focal spot and the solid lines indicate thetemperature of the surface of the target just before it is hit again bythe focal spot. The black dotted line represents the melting temperatureof tungsten (3,422° C.). There are four sets of lines on each graph,representing targets of varying radius. The uppermost solid/dotted linerepresents a target with a radius of 10 cm, and the lowermostsolid/dotted line represents a target with a radius of 50 cm. From theseplots it can be seen that in order to maintain a high output over timescales of around 1 s, the target radius must be of an appropriate size,or the heat must otherwise be distributed over a larger surface area,e.g. by a reciprocating motion of the focal spot along the targetcylinder axis.

From the above analysis, two general statements can be made:

-   -   The maximum dose rate depends solely on the surface speed of the        target; and    -   The maximum dose that can be delivered, at a fixed dose rate and        focal spot length, depends only on the area the heat is spread        on the target surface.

Table 3 shows the variation of exposure time (and therefore maximumdose) for targets of two different radii. These values are given for a500 mm distance between the collimator and focal spot on the target, theGray values are peak entrance doses for a dosimetry phantom positioneddirectly in front of the collimator.

TABLE 3 Exposure Exposure Exposure Time at Dose at Time at Dose at Timeat Dose at Radius 250 kW 250 kW 500 kW 500 kW 715 kW 712 kW [cm] [s][Gy] [s] [Gy] [s] [Gy] 30 7.00 360.5 1.80 185.4 0.91 133.8 50 19.39998.6 4.89 503.7 2.45 360.2

The maximum achievable tube power (given the assumptions made) is 712kW. With a target with a diameter of 1 m the maximum dose which can bedelivered is around 360.2 Gray. Whilst 250 kW and 500 kW power levelsmay achieve a greater total dosage, the dose rate (i.e. Gy/s) issignificantly lower. High dose rates, however, are essential in clinicalmicro-beam treatments, in order to avoid blurring of the dosedistribution e.g. by cardiovascular motion.

Preferably the target has a smaller diameter than 1 m, as there aresignificant technical, energy consumption and safety issues associatedwith spinning large objects at high frequencies. One method of reducingthe diameter of the target is to translate the focal spot of theelectron beam along the surface of the target in use, as discussed abovein relation to FIGS. 2A and 2B.

A further option to increase the dose and dose rate is to increase thefocal spot length and width, whilst keeping the collimator dimensionsconstant. Therefore the amount of x-ray radiation generated may bedoubled, whilst still allowing the collimator to produce micro-beamradiation. Increasing the focal spot length and width by a factor of 2would give a factor of 4 increase in dose rate and a factor of 2increase in dose. The focal spot would still be substantially the sameshape as the slits in the collimator, but would be larger in size. Thebeam shape would be slightly deteriorated. FIG. 16 shows equivalentprofiles to those of FIG. 9, but for the larger focal spot size. Whilstthe beam-penumbra is wider than before (FIG. 9) it might still beacceptable for radiological purposes. It may also be possible toincrease the width and length of the focal spot by a factor of 3.

One more option to increase the dose and dose rate is to move thecollimator closer to the surface of the target. In principle 200 mm canbe used, and would give a factor of 6.25 increase in dose and dose rate.However there would be a higher beam divergence, and therefore the depthdose curve would not be as favourable. Also beam width and beam-to-beamspacing would more rapidly increase with distance from the collimator.

Table 4 provides a comparison of various key parameters betweenmicro-beam radiation as produced by a synchrotron and micro-beamradiation as produced by an x-ray tube according to the presentinvention:

TABLE 4 European Synchrotron (ESRF) X-ray tube Dose rate 15,000 Gy/s;Average: 147 Gy/s Effectively*: 375 Gy/s Upper limit: ≈1200 Gy/s Beamdivergence Parallel Beams; Divergent beam; Steep beam penumbras Forexample, in a 100 mm deep phantom: ctc of 400-480 μm; beam penumbra ofup to 10 μm Depth dose curves Depth independent Depth dependent, butbeginning at about 500 mm similar to the synchrotron Energy consumption≈2.5 MW continuously 1 MW-4 MW for a few seconds Beam switchingMechanical, therefore Electric (no current = no beam); mechanismdifficult and slow fast Movability Immovable Can be moved around patient*The field height at the European Synchrotron is about 500 μm. Thereforepatients need to be scanned vertically through the beam. The effectivedose rate is hence lower than the nominal 15,000 Gy/s

Production of High Brilliance X-rays

The system 200 shown schematically in FIGS. 2A and 2B and discussed inthe above subsection, generates, accelerates and electromagneticallyshapes an electron beam 202 that hits the fast rotating, typicallytungsten, cylindrical target 205 in a thin focus line, i.e. a focalspot, with a very large aspect ratio h/δ, where h and δ are the lengthand width of the focal spot 206, respectively. The surface velocity ofthe focal spot across the target surface in the width direction is v.Changes in the physics of the target heating at high values of v andsmall spot widths advantageously permit a significant increase inelectron beam current density without raising the focal spot temperatureabove the melting point of tungsten.

In conventional rotating anode x-ray tubes, heat conduction limits thetemperature increase in the focal spot. An electron beam power P_(cond)is absorbed at a focal spot surface area A=δh and almost completelyconverted into heat. The heat is dissipated by heat conduction and thefocal spot temperature increase ΔT during an exposure time Δt isproportional to the electron beam intensity P_(cond)/A at the focal spot(Oosterkamp W. Calculation of the Temperature Development in a ContactHeated in the Contact Surface, and Application to the Problem of theTemperature in a Sliding Contact. Journal of Applied Physics. 1948;19(12):1180-1; and Oppelt A, Kutschera W, Behner H, Bernhardt J,Neumeier E, Ponnath P, et al. Imaging systems for medical diagnostics.2nd edition ed. Erlangen: Publicis MCD; 2005):

${\Delta T} = {\frac{2P_{cond}}{A}\sqrt{\frac{\Delta t}{\pi k\rho c}}}$

where k, ρ and c denote heat conductivity, density and heat capacity ofthe target material. For a rotating anode Δt will be δ/v and, assuming afixed maximum temperature rise ΔT_(max) the target can withstand, themaximum electron beam power is:

${P_{cond} = {\gamma_{1}h\sqrt{v\delta}}},{\gamma_{1}\sqrt{\frac{1}{4}\Delta T_{\max}^{2}\pi k\rho c}}$

However, as the previous equation for ΔT is a solution of the heatequation with Neumann boundary conditions, it only assumes a surfaceheating at an electron beam intensity of P_(cond)/A. The range ofelectrons in the target material is completely ignored, which is a validassumption as long as the heat diffusion length l_(d) during electronbeam exposure time Δt,

${l_{d} = {2\sqrt{\frac{k\Delta t}{\rho c}}}},$

is much larger than the electron range l_(e), l_(d)>>l_(e).

This changes for large surface velocities v, narrow spot widths δ andlarge electron penetration depths at high acceleration voltages, though.If the electron range l_(e) is significantly larger than the heatdiffusion length l_(d), l_(e)>>l_(d), the heating of the target materialis limited by the heat capacity only. A volume element δV receiving theheating power δP by electron absorption, heats according to

δPΔt=ρδVcΔT.

For a fixed maximum temperature increase ΔT_(max) this leads, incontrast to the above equation for P_(cond), to a maximum electron beampower of

P _(cap)=γ₂ vld,γ ₂ =ρcΔT.

Here the electron penetration depth is denoted by d and depends on theelectron beam energy and the anode material. An accurate definition of dis provided in the Appendix. Importantly, P_(cap) does not depend on thefocal spot width δ. Hence a reduction in focal spot width does notimpact on the maximum possible electron beam power anymore. Theintensity P_(cap)/A of the electron beam can be increased ad libitum byreducing the focal spot width and is only limited by lateral scatteringof electrons in the target which is approximately given by δ_(min)≈d/3(see also Appendix, “Estimation of δ_(min)”).

The transition from the conventional heat conduction limit(l_(d)>>l_(e)) to the heat capacity limit (l_(e)>>l_(d)) occurs whenP_(cap)=P_(cond). The surface velocity v_(t) at this transition is

${v_{t} = {\frac{\pi k}{4\rho c} \cdot \frac{\delta}{d^{2}}}},$

and the maximum possible increase in brightness, as compared to the heatconduction limit, is equal to the ratio of P_(cap) and P_(cond) at thesmallest possible focal spot width δ_(min),

$\frac{P_{cond}}{P_{cap}} = {\frac{B_{cond}}{B_{cap}} = {B{\sqrt{\frac{\rho c}{\pi k}} \cdot \sqrt{\delta_{\min}v}}}}$

As discussed in the subsection above, anode surface velocities of up toaround 200 m/s can be reached in specialized but conventional rotatinganode x-ray tubes. However, velocities of up to around 1000 m/s arepossible with a system of the type shown in FIG. 2. FIG. 17 shows themaximum possible power of an electron beam hitting a rotating tungstentarget in a 1 cm long (h) focal spot in dependence on the focal spotwidth δ and the electron beam energy. The surface velocity of the anodeis assumed to be v=200 m/s and the maximum temperature increase ΔT=2500K. The contour lines show the transition from heat conduction limit toheat capacity limit at v=200 m/s and selected other surface velocities.While the maximum electron beam power at a given voltage depends on thefocal spot width in the heat conduction limit, it is independent of thefocal spot width at a given voltage in the heat capacity limit. However,the maximum electron beam power at a given spot width becomes energydependent in the heat capacity limit, since it is influenced by theelectron penetration depth d. A final physical lower limit for the focalspot width is given by lateral electron scattering. This is indicated bythe white area at the bottom of the graph with δ<δ_(min).

A system of the type shown in FIG. 2 operating in the heat capacitylimit (hereafter termed a “line-focus tube”—LFT), not only enables thetranslation of several highly promising technical developments inmedicine into clinical practice, but can also promote and simplify x-rayapplications in various other areas where high brilliance is essential.For these applications, the system can be used with or without thecollimator 212, and also can be used with or without the relativemovement of the focal spot 206 along the direction 208 parallel to thecylindrical axis of the target 205. In high resolution x-ray imaging,for example, resolution is limited by the size of the source andcontrast resolution is proportional to N^(−1/2). The LFT facilitates thefast acquisition of high resolution 2D and 3D images.

Indeed, as previously mentioned, phase contrast imaging can provide highcontrast and high resolution images. However, to observe interference acoherent radiation source is needed. Conventionally suitable spatialcoherence can be obtained using gratings, but these absorb a substantialpart of the initial x-ray beam intensity. This can be avoided by usingthe LFT as a spatially coherent source in the first place whose photonflux is comparable to that of rotating anode x-ray tubes used inconventional x-ray imaging. FIG. 18 compares the various existing x-raysources in terms of coherence lengths and photon flux, and shows thatthe LFT competes in photon flux and spatial coherence perpendicular tothe long axis of the focal spot with Inverse Compton Scattering sources.See the Appendix for derivations of the comparison of FIG. 18.

While the invention has been described in conjunction with the exemplaryembodiments described above, many equivalent modifications andvariations will be apparent to those skilled in the art when given thisdisclosure. Accordingly, the exemplary embodiments of the invention setforth above are considered to be illustrative and not limiting. Variouschanges to the described embodiments may be made without departing fromthe spirit and scope of the invention.

APPENDIX

Derivation of Heat Transport in Heat Capacity Limit

We here derive the target heating in the heat capacity limit, i.e. weassume no heat transport during the time of heating. In practice both,heat conduction and electron energy transport contribute to the heatdissipation. Especially at conditions where the heat diffusion and theelectron range are of similar size, the temperature increase at thefocal spot in practice is lower than calculated by either of the twomodels.

A volume element δV receiving over a time dt the thermal power δPincreases in temperature dT according to

δPdt=ρcδVdT,

FIG. 19A shows the geometry in the LFT. The electron beam moves withvelocity v along x relative to the target surface. Electrons arestatistically scattered and absorbed in the target material and create apower distribution δP/δV(x,y,z). This distribution is time dependent,since the beam is moving along x, i.e. x=x(t). The total temperatureincrease ΔT that a volume element δV experiences can be calculated via

${\overset{\frac{\Delta t}{s}}{\int\limits_{\frac{\Delta t}{2}}}{\frac{\delta P}{\delta V}\left( {{x(t)},y,z} \right)dt}} = {\rho c\Delta T}$

Assuming that the length h of the focal spot is much larger than theelectron scattering range and that δP/δV does not depend on y and

${\frac{\delta P}{\delta V}\left( {{x(t)},y,z} \right)} = {{\frac{1}{h}\frac{\delta^{2}P}{\delta x\delta z}\left( {{x(t)},z} \right)} = {\frac{{\overset{.}{N}}_{el}}{l}{\left\langle {\frac{\delta^{2}E_{el}}{\delta x\delta z}\left( {{x(t)},z} \right)} \right\rangle.}}}$

We replace the power P by the number of electrons per time N_(el) timesthe average kinetic energy absorption of an electron E_(el). Integrationof this expression in the previous integral leads to

${\frac{{\overset{.}{N}}_{el}}{vl}{\overset{\frac{\Delta x}{2}}{\int\limits_{\frac{\Delta x}{2}}}{\frac{\delta^{2}E_{el}}{\delta x\delta z}\left( {x,z} \right)dx}}} = {{\frac{{\overset{.}{N}}_{el}}{vl}\left\langle {\frac{\delta E_{el}}{\delta z}(z)} \right\rangle} = {{\frac{P}{vl}\frac{1}{E_{el}}\left\langle {\frac{\delta E_{el}}{\delta z}(z)} \right\rangle} = {\rho c\Delta T}}}$

The maximal temperature increase is given where

$\left\langle {\frac{\delta E_{el}}{\delta z}(z)} \right\rangle$

reaches its maximum and hence the quantity

$E_{el}/\left\langle {\frac{\delta E_{el}}{\delta z}(z)} \right\rangle$

max can be identified with the electron penetration depth d. Theelectron penetration depth can be calculated in Monte Carlo simulations.The following Table A1 presents values computed in the Geant4™ tool setversion 10.0 p03 using the Penelope™ low energy physics libraries(https://geant4.web.cern.ch/geant4/). For electrons with a kineticenergy of 600 keV FIG. 19B shows

$\left\langle \frac{\delta E_{el}}{\delta z} \right\rangle$

as a function of depth z.

TABLE A1 E [keV] 20 50 100 700 500 1000 d [μm] 0.322 1.28 3.99 11.2 43.7107

Estimation of δ_(min)

The achievable focal spot width depends on the possibility to focus theelectrons to a focal spot with a high aspect ratio h/δ, and on thescattering of the electrons in the target material.

In order to calculate the scattering limit of the focal spot size weused Geant4™ to simulate an infinitely small beam hitting a tungstensurface perpendicular in a point producing bremsstrahlung as shown inFIG. 20A. At an observer point, photon trajectories were recorded andthe apparent source distribution in the x′-y′ plane calculated. Theresult is shown in FIG. 20B for a 100 keV electron beam. The full widthat half maximum (FWHM) of the source measures only between 10 and 80 nm.However, due to electron scattering there is a relatively highbackground noise. More conservatively the source could be defined as thewidth (FWHM) of the lateral electron scattering which is in the order ofd/3 (e.g. 1.6 μm in tungsten for 100 keV electrons).

Estimation of Photon Fluxes and Spatial Coherences

FIG. 18 compares various sources in terms of coherence length and photonflux. The delineated performance regions are only a rough estimate,though based on data of typical existing sources.

The performance of the x-ray tubes was estimated at the Kα1 absorptionedge of tungsten, i.e. at a photon energy of 59.3 keV and a wavelength λof 20.7 μm. The distance r from the source was assumed to be 1 m. For asource with random phase distributions, the spatial coherence lengthl_(s) can be approximated by

${l_{s} = {\lambda \cdot \frac{r}{\delta}}},$

where δ is the source diameter. The flux at distance r, x-ray tube powerP and acceleration voltage U can be calculated from

${\Phi = {\eta\frac{P}{eU}{f_{\Delta\Omega} \cdot \frac{1}{r^{2}}}}},$

where e denotes the electron charge, η the electron conversionefficiency as the number of Kα1 fluorescence photons per electron andf_(ΔΩ) is the fraction of photons emitted in a certain angle interval.The electron conversion efficiency strongly increases with accelerationvoltage U for U>59.3 keV and was calculated in Monte Carlo simulationsin Geant4™ at various electron energies as shown in FIG. 21. Thefraction of photons emitted per angle interval resembles a completelyisotropic source,

f≈2·10⁻⁷ mrad⁻².

The parameters η and f_(ΔΩ) are the same for all x-ray tubes with atungsten target. Only P, U and the focal spot size vary.

A Varian HPX-160-11 stationary anode x-ray tube with U=160 kV a focalspot size of 0.4 mm at 800 W or 1.0 mm at 1800 W is an example of aconventional x-ray tube. This leads to a coherence length of 51.8 nm and20.7 nm and a photon flux of 3.25·10⁶ mm⁻² s⁻¹ and 7.32·10⁶ mm⁻² s⁻¹ atthe small and large focal spot size, respectively.

A typical rotating anode tube is the Siemens™ Straton Tube with U=140kV, P=100 kW and a focal spot size of 1.8×7.2 mm. This leads to acoherence length l_(s) of 15 nm in 1 m distance from the source and aphoton flux of around 2.8·10⁸ mm⁻² s⁻¹. (Oppelt et al., ibid.)

Microfocus tubes typically operate at an electron beam power of 4-40 W,(e.g. Hamamatsu™ microfocus x-ray tube series) at focal spot sizesbetween 5 and 80 μm with acceleration voltages between 20 and 160 kV.The coherence length is in the order of 0.2 to 5.0 μm and the photonflux will be between 2·10⁴ and 2·10⁵ mm⁻² s⁻¹.

Metal jet x-ray tubes employ other target materials and therefore theconversion efficiency and the fluorescence lines are different. As anexample is Excillum™ metal jet x-ray tubes. The brilliance is reportedto be between 2.6·10¹⁰ and

$10 \cdot 10^{10\frac{1}{s{mm}^{2}m{rad}^{2}}}$

per spectral line and the source size between 5 and 20 μm. At 5 μm focalspot size the flux is between 6.5·10⁵ and 2.5·10⁶ mm⁻² s⁻¹.Unfortunately metal jet x-ray tubes operate at lower photon energies.However, to compare coherence lengths a wavelength of 20.7 μm can beassumed, which leads to a coherence length of around 4 μm.

For the inverse Compton Scattering source at the Massachusetts Instituteof Technology a beam brilliance of

$2 \cdot 10^{15\frac{1}{s{mm}^{2}m{rad}^{2}0.1\%{bw}}}$

and a source size of 2 times 6 μm are reported (Graves W, Brown W,Kaertner F, Moncton D. MIT inverse Compton source concept. NuclearInstruments and Methods in Physics Research Section A: Accelerators,Spectrometers, Detectors and Associated Equipment. 2009;608(1):S103-S5.). At a source distance of again 1 m this infers a photonflux of 2.4·10¹⁰ mm⁻² s⁻¹ at a coherence length of 3 to 10 μm.

The best performance is achieved by 3^(rd) generation synchrotrons witha brilliance between 10²⁰ and

$10^{24\frac{1}{s{mm}^{2}m{rad}^{2}0.1\%{bw}}}$

(Huang Z. Brightness and coherence of synchrotron radiation and FELs.MOYCB101, Proceedings of IPAC2013, Shanghai, China. 2013) and a sourcediameter of around 50 μm (e.g. Lengeler B, Schroer C G, Kuhlmann M,Benner B, Günzler T F, Kurapova O, et al. Refractive x-ray lenses.Journal of Physics D: Applied Physics. 2005; 38(10A):A218). The distancebetween source and experiment is usually much larger than 1 m. Thereforewe assume, deviating from the previous estimates, a source distance r of40 m. There the flux is between 10¹⁴ and 10¹⁸ mm⁻² s⁻¹ and the coherencelength around 15 μm at a photon energy of 60 keV.

1. An x-ray radiation production system having: a source of acceleratedelectrons; an electron focusing component configured to focus theelectrons provided by the source; and a target which produces x-rayswhen electrons impinge thereon from the source; wherein the electronfocusing component is configured to focus the electrons provided by thesource such that they impinge at a focal spot having a width δ formed ona surface of the target; and wherein the focusing component isconfigured to move the electron beam relative to the target such thatthe focal spot moves across the target surface in the width direction,and/or the target is movable relative to the focusing component suchthat the focal spot moves across the target surface in the widthdirection, the surface velocity of the focal spot across the targetsurface in the width direction being greater than v_(t) where:${v_{t} = {\frac{\pi k}{4\rho c} \cdot \frac{\delta}{d^{2}}}},$ k, ρ andc denoting respectively the heat conductivity, the density and the heatcapacity of the target material, and d denoting the electron penetrationdepth in the target material.
 2. The system of claim 1, wherein thewidth δ of the focal spot is less than 100 μm.
 3. The system of claim 1,wherein the target is cylindrical, and the target rotates around itsaxis to move the target surface relative to the focusing component. 4.The system of claim 1, wherein the electrons are accelerated with anacceleration voltage of at least 40 kV. 5.-15. (canceled)
 16. A methodof operating the system of claim 1, having the steps of: providingelectrons from the electron source; focusing the electrons using theelectron focusing component such that they impinge at a focal spothaving a width δ formed on the surface of the target, thereby producingx-rays; and moving the electron beam relative to the target such thatthe focal spot moves across the target surface in the width direction,and/or moving the target relative to the focusing component such thatthe focal spot moves across the target surface in the width direction,the surface velocity of the focal spot across the target surface in thewidth direction being greater than v_(t) where:${v_{t} = {\frac{\pi k}{4\rho c} \cdot \frac{\delta}{d^{2}}}},$ k, ρ andc denoting respectively the heat conductivity, the density and the heatcapacity of the target material, and d denoting the electron penetrationdepth in the target material.
 17. The method of claim 16, wherein theproduced characteristic x-rays of a spectral line of the target materialat 60 keV may have a spatial coherence length of at least 5 μm at 1 mdistance from the target.
 18. The method of claim 16, wherein theproduced characteristic x-rays of a spectral line of the target materialat 60 keV may have a photon flux of at least 1·10⁶ mm⁻² s⁻¹ at 1 mdistance from the target.
 19. A method for phase contrast imaging,having the steps of: performing the method of claim 16; and performingphase contrast imaging using the produced x-rays as a source ofillumination. 20.-23. (canceled)